24 Questions
How is overflow determined by the CPU for B2T (signed) addition?
By comparing the last two carries
Can the same method be used for B2O addition?
No, a different method is used for B2O addition
What method is universally used for encoding signed integers in all modern hardware?
Two's complement
How is an integer negated in B2T (Two’s complement)?
By inverting all the bits
How are numbers encoded in B2O added when one operand is negative and one is non-negative?
By adding a carry bit back to the result with a second addition
How does the CPU compare the last two carries to determine overflow for two’s complement operations?
Using an XOR gate to compare the carries
What is the smallest unit of memory in a computer system?
Byte
How many different values can be encoded by a bit string with n bits?
$2^n$
What is the range of values which can be encoded by a B2U number of n bits?
$0$ to $2^n - 1$
What is a byte?
8 bits
What bit value is used as the first carry to add two B2U numbers?
$0$
Are instructions stored as bit strings in a computer system?
Depends on the computer system
In B2T (Two's complement) encoding, how is an integer negated?
By inverting all the bits and adding 1
For B2O (One's complement) addition, when adding numbers with one negative and one non-negative operand, how does the hardware handle the addition differently?
It performs a second addition with the last carry bit added back to get the final result
How does a CPU determine overflow for B2T (Two's complement) operations?
By examining the carry into and out of the most significant bit
Why is Two's complement encoding universally used in modern hardware for signed integers?
It avoids having two representations of 0
How can subtraction be performed in Two's complement by using inversion of one operand and a first carry of 1?
By inverting all bits of one operand and adding it to another
What gate is used by the CPU to compare the last two carries to determine overflow in Two's complement operations?
AND gate
How many different ways of encoding signed integers were discussed in the class?
Three
What is the range of values that can be encoded by a B2O (offset binary) number of n bits?
$-2^{n-1}$ to $2^{n-1} - 1$
What is the main difference between B2S and B2T methods of encoding signed integers?
B2S has a universal definition, while B2T's definition varies.
In a computer system, how is memory typically organized?
In a hierarchical structure with different levels of memory hierarchy
What is the number of bits required to encode $128$ different values using a bit string?
$7$
What type of data/information is stored as bit strings in a computer system?
Both numerical and textual data
Test your knowledge of computer components, memory units, bit strings, data storage, instructions, and memory organization. Explore the concept of a word of memory and its size variations in different systems.
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